As an illustrative vehicle we employ a generalized Vicsek
model [1]} with two additional features: 1) tunable influence
weight of one particle over another (i.e., leaders have larger influence) and
2) particle memory. We show that, by analyzing the effects of 1) and 2) on the
three modes of information flow, intrinsic information flow exists whenever the
motion of an agent depends on another with nonzero weight, as does transfer
entropy and time-delayed mutual information. Shared and synergistic
information, however, can occur when agents mutually influence each other and
synergistic information only occurs in such cases. These results extend
previous studies on modes of information flow in finite-state hidden Markov
models by introducing Vicsek models that are fundamental to understanding
collective motion and exhibit distinct modes of information flow. Moreover, we
probe the effect of agent memory and the effect of more than two interacting
agents on the different modes of information flow and their role in collective
behavior.
